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Code Katas

Focused, repeatable coding exercises designed to build fluency in simulation-backed probability reasoning. Complete each kata multiple times until the setup feels automatic.

Kata 1: Birthday Collision Simulator​

Time limit: 20 minutes
Goal: Estimate the probability of at least one repeated birthday in a room of size n
Setup: Write a function that simulates k rooms and compares the empirical estimate with the theoretical complement calculation

Repeat until: You can explain why the simulation and the complement formula should agree approximately.

Kata 2: Bayes Update Engine​

Time limit: 15 minutes
Goal: Implement a helper that computes posterior probability from prior, sensitivity, and false-positive rate
Setup: Feed it several low-base-rate scenarios and print prior, evidence rate, and posterior clearly

Repeat until: You can describe every term in the update without mixing up direction.

Kata 3: Expectation by Indicators​

Time limit: 20 minutes
Goal: Simulate and estimate the expected number of fixed points in random permutations
Setup: Count fixed points directly, then explain the indicator-variable solution on paper

Repeat until: You can connect the code result to the linearity argument.

Kata 4: LLN and CLT Sampler​

Time limit: 25 minutes
Goal: Generate repeated sample means from a non-Normal distribution and observe stabilization plus approximate Normality of the sample mean
Setup: Use a skewed base distribution, vary sample size, and record mean/spread behavior

Repeat until: You can say what the LLN explains and what only the CLT explains.

Completion Standard​

  • Can implement each kata within the time limit
  • Can explain the theory behind each simulation without rereading the concept page
  • Can compare empirical output to theoretical expectations and describe the mismatch if one appears